Problems and Solutions on Bohr's Atomic Model

Problem and solution

When the electron in hydrogen atom jumps from second orbit to first orbit, a certain wavelength is emitted. When the electron jumps from the third orbit to first orbit, what is the new wavelength emitted in terms of the first wavelength?

We can solve this problem basing on the derivation is that we made for the reciprocal of the wavelength in terms of the Redberg constant. By applying the given condition in the problem in two different equations and by simplifying them we can solve the problem as shown below.

Problem and solution

What is the ratio of largest to shortest wavelengths in the Balmer series of the hydrogen spectrum?

We can solve this problem also basing on the derivation that we made for the reciprocal of the wavelength in terms of principal quantum numbers. For the wavelength to be maximum, the corresponding energy has to be minimum. It is possible only when the electronic jumping from the third orbit to second orbit.

Further wavelength to be minimum, the corresponding energy has to be maximum. This is possible when their electron is jumping from infinite orbit to second orbit. The corresponding equation is written in the problem is solved as shown below.

Problem and solution

In a hydrogen atom electron is jumped from the fifth orbit to first orbit. What is the recoil speed of the hydrogen atom in this process?

As the electronic jumping from higher orbit to lawyer orbit, there is some emission of energy. This emitted energy will have a certain wavelength. To compensate the jerk that is generated by this emitted energy, nuclear is most with a little bit velocity and here we are going to calculate that velocity. By substituting the wavelength that we have derived in the de Broglie concept we can derive the equation for the velocity of the nucleus as shown below.

Problem and solution

If the wavelength of the first member of the Balmer series in the hydrogen spectrum is 6564 Å, what will be the wavelength of the second member of the Balmer series?

We can solve this problem by writing the equation for the reciprocal of the wavelength using the atomic model. By comparing the given two conditions we can get the answer as shown below.